Lab 2 loading library

Reading input

1. Scatter plot dependence of Palmitic on Oleic, linolenic not classed and classed

Analysis: The second graph is easier to analysis than compared to first one, the perception problem highlighted here is the difference in the channel capacity of human preception. Its difficult to distinguish between different shades of blue while its easier to distinguish between differnet hues (channel capacity is here). Eg: The difference in values say at 400 to 900 is very similar in first graph.

2. Scatter plot dependence of Palmitic on Oleic, linolenic split by different attributes

ggplot(data = olive_data, aes(x = oleic, y = palmitic)) + geom_point(aes(colour = cut_interval(linolenic, n = 4))) + ggtitle("Scatter plot of palmitic vs. oleic coloured by 4 intervals of linolenic")

ggplot(data = olive_data, aes(x = oleic, y = palmitic)) + geom_point(aes(size = cut_interval(linolenic, n = 4))) + ggtitle("Scatter plot of palmitic vs. oleic sized by 4 intervals of linolenic")
## Warning: Using size for a discrete variable is not advised.

ggplot(data = olive_data, aes(x = oleic, y = palmitic)) + geom_point() +  geom_spoke(aes(angle = as.numeric(cut_interval(linolenic, n = 4))*10), radius = 50) + ggtitle("Scatter plot of palmitic vs. oleic spoke angles by 4 intervals of linolenic")

Analysis: The discretized Linolenic with color was the easiest to detect boundary. This is becuase the channel capacity of detection is in the order of color>direction>size

3. Scatter plot dependence of Oleic on Eicosenoic, Region split by different attributes

ggplot(data = olive_data, aes(x = oleic, y = eicosenoic)) + geom_point(aes(colour = as.numeric(Region))) + ggtitle("Scatter plot of palmitic vs. oleic, coloured by region as number")

ggplot(data = olive_data, aes(x = oleic, y = eicosenoic)) + geom_point(aes(colour = Region)) + ggtitle("Scatter plot of palmitic vs. oleic, coloured by region as factors")

Analysis: Using a factor simply as number assumes that the difference between region is an increment of one, eg: Cat->Dog->Human the difference is one unit among the three, while treating them as factor does not assuming any step increment. The Preattentive pattern emerged here due to distinct colour.

4. Scatter plot dependence of Oleic on Eicosenoic, linoleic not classed and classed and 27 objects

ggplot(data = olive_data, aes(x = oleic, y = eicosenoic)) + geom_point(aes(colour = cut_interval(linoleic, n = 3), shape = cut_interval(palmitic, n = 3), size = cut_interval(palmitoleic, n = 3)))
## Warning: Using size for a discrete variable is not advised.

Analysis: Its very hard to distinguish between 27 types of combination due to no clear boundary between the regions, the perception problem the channel capacity does not follow mathematical summation that is three shades of colour + three types of shapes != channel capacity of 3 shapes and 3 colours in a chart.

5. Scatter plot dependence of Oleic on Eicosenoic, linoleic not classed and classed and 27 objects

ggplot(data = olive_data, aes(x = oleic, y = eicosenoic)) + geom_point(aes(colour = Region, shape = cut_interval(palmitic, n = 3), size = cut_interval(palmitoleic, n = 3)))
## Warning: Using size for a discrete variable is not advised.

Analysis: According to Treisman’s theory, in case of perceiving a stimulus, features are “registered early, automatically, and in parallel, while objects are identified separately” and at a later stage in processing. The explaination is as follows: Any object’s feature will be processed parallely and serially, if an object can be split with reasonable boundary (say shape) then our brain process the individual features seperately, thus identify a boundary becomes easy in this chart compared to above.

6. piechart of oils vs. region

olive_data_sum <- olive_data %>% group_by(Region) %>% summarise(palmitic = sum(palmitic),
                                                     palmitoleic = sum(palmitoleic),
                                                     stearic = sum(stearic),
                                                     oleic = sum(oleic),
                                                     linoleic = sum(linoleic),
                                                     linolenic = sum(linolenic),
                                                     arachidic = sum(arachidic),
                                                     eicosenoic = sum(eicosenoic))


olive_data_sum_long <- melt(olive_data_sum, id.vars = c("Region"))

olive_data_sum_long %>% group_by(Region) %>% plot_ly(labels = ~variable, values = ~value, 
                                                     type = 'pie', showlegend = FALSE) %>% layout(title = 'Total oils by region', 
                                                                                                  xaxis = list(showgrid = FALSE, zeroline = FALSE, showticklabels = FALSE), yaxis = list(showgrid = FALSE, zeroline = FALSE, showticklabels = FALSE))

Analysis: The plot does not conform to the practices under good visualization, it is generally not advised to use piechart because angles are harder to detect than size. Not having clear lables/legend simply adds to more overhead to process the information

7. 2D density contour plot

ggplot(olive_data, aes(x = linoleic, y = eicosenoic)) + geom_point(aes(colour = Region)) + geom_density_2d()

ggplot(olive_data, aes(x = linoleic, y = eicosenoic)) + geom_point(aes(colour = Region))

Analysis: As evident from the two plots the density plot suggests a clusters being formed while the simple scatter plots coloured by region suggests a simpler cluster

Assignment 2

1. Loading the input xlxs file

baseball <- read.xlsx("baseball-2016.xlsx", sheetName = "Sheet1")

Analysis: Yes its reasonable to scale the data (perform dimensionality reduction) since more than visualizing more than 4 feaures is not advised.

2. Non mertic MDS (ISOMDS)

distance <- dist(baseball[, !names(baseball) %in% c("Team", "League")] , method = "minkowski")
fit <- isoMDS(distance, k = 2, maxit = 100)
## initial  value 12.061782 
## final  value 12.060912 
## converged
baseball$MDS1 <- fit$points[,1]
baseball$MDS2 <- fit$points[,2]

# plotly plot
baseball %>% plot_ly(type = "scatter", 
                     mode = "markers", 
                     colors = "Set1",
                     showlegend = T) %>% add_trace(x = ~MDS1, y = ~MDS2, color = ~League, text = ~Team) %>% layout(title = "Non Metric MDS plot")

Analysis: None of the axis make a clear boundary between the two Leagues. The outlier teams are as follows: Milwaukee Brewers, Boston Red Sox, Los Angeles Angels, Philadelphia Philies, San Diego Padres.

3. Shepard plot of MDS

sh <- Shepard(distance, fit$points)
Original_Dist <-as.numeric(distance)
MDS_Dist <- as.numeric(dist(fit$points))

rownames(baseball) <- baseball$Team

n=nrow(fit$points)
index=matrix(1:n, nrow=n, ncol=n)
index1=as.numeric(index[lower.tri(index)])

n=nrow(fit$points)
index=matrix(1:n, nrow=n, ncol=n, byrow = T)
index2=as.numeric(index[lower.tri(index)])

plot_ly()%>%
  add_markers(x=~Original_Dist, y=~MDS_Dist, hoverinfo = 'text', name = "Datapoints",
        text = ~paste('Obj1: ', rownames(baseball)[index1],
                      '<br> Obj 2: ', rownames(baseball)[index2]))%>%
  #if nonmetric MDS inolved
  add_lines(x=~sh$x, y=~sh$yf, name="Stress")

Analysis: The datapoints away from the 45degree line(orange) are the the pairs of points where the MDS was not successful.

4. Plotting MDS axis with variables of baseball dataset

MDS_plotter <- function(MDS_axis, Col){
  df <- cbind(baseball[[MDS_axis]], baseball[[Col]], baseball$League, baseball$Team)
  df <- as.data.frame(df)
  names(df) <- c(eval(MDS_axis),eval(Col), "League", "Team")
  df$League <- as.character(df$League)
  
    # plotly plot
  y_title <- list(title = Col)
  x_title <- list(title = MDS_axis)
   
  plot_return <- df %>% plot_ly(type = "scatter", mode = "markers", colors = "Set1", showlegend = T) %>% 
    add_trace(x = df[,1], y = df[,2], color = ~League, text = ~Team) %>% 
    layout(title = "Plot of MDS axis vs. variable", yaxis =y_title, xaxis=x_title)
  return(plot_return)
}

# Plotting MDS on all numeric columns
# MDS axis 1
# MDS_plotter("MDS1", "Won")
# MDS_plotter("MDS1", "Lost")
# MDS_plotter("MDS1", "Runs.per.game")
# MDS_plotter("MDS1", "HR.per.game")
# MDS_plotter("MDS1", "AB")
# MDS_plotter("MDS1", "Runs")
# MDS_plotter("MDS1", "Hits")
# MDS_plotter("MDS1", "X2B")
# MDS_plotter("MDS1", "X3B")
# MDS_plotter("MDS1", "HR")
# MDS_plotter("MDS1", "RBI")
# MDS_plotter("MDS1", "StolenB")
# MDS_plotter("MDS1", "CaughtS")
# MDS_plotter("MDS1", "BB")
# MDS_plotter("MDS1", "SO")
# MDS_plotter("MDS1", "BAvg")
# MDS_plotter("MDS1", "OBP")
# MDS_plotter("MDS1", "SLG")
# MDS_plotter("MDS1", "OPS")
# MDS_plotter("MDS1", "TB")
# MDS_plotter("MDS1", "GDP")
# MDS_plotter("MDS1", "HBP")
# MDS_plotter("MDS1", "SH")
# MDS_plotter("MDS1", "SF")
# MDS_plotter("MDS1", "IBB")
# MDS_plotter("MDS1", "LOB")
# 
# # MDS axis 2
# MDS_plotter("MDS2", "Won")
# MDS_plotter("MDS2", "Lost")
# MDS_plotter("MDS2", "Runs.per.game")
# MDS_plotter("MDS2", "HR.per.game")
# MDS_plotter("MDS2", "AB")
# MDS_plotter("MDS2", "Runs")
# MDS_plotter("MDS2", "Hits")
# MDS_plotter("MDS2", "X2B")
# MDS_plotter("MDS2", "X3B")
# MDS_plotter("MDS2", "HR")
# MDS_plotter("MDS2", "RBI")
# MDS_plotter("MDS2", "StolenB")
# MDS_plotter("MDS2", "CaughtS")
# MDS_plotter("MDS2", "BB")
# MDS_plotter("MDS2", "SO")
# MDS_plotter("MDS2", "BAvg")
# MDS_plotter("MDS2", "OBP")
# MDS_plotter("MDS2", "SLG")
# MDS_plotter("MDS2", "OPS")
# MDS_plotter("MDS2", "TB")
# MDS_plotter("MDS2", "GDP")
# MDS_plotter("MDS2", "HBP")
# MDS_plotter("MDS2", "SH")
# MDS_plotter("MDS2", "SF")
# MDS_plotter("MDS2", "IBB")
# MDS_plotter("MDS2", "LOB")

# Best plots are with MDS-2 with variables HR.per.game and HR
MDS_plotter("MDS2", "HR.per.game")
MDS_plotter("MDS2", "HR")

Analysis: For batter, the three metric “Batting average”, “Runs batted in (RBI)” and “Home Runs (HR)” determine the ranking. For the pitchers its “Stike Outs(SO)” and “Wins”. Thus MDS1 axis of our MDS helps to seperate leagues on the batting performance. One thing to note is unlike PCA, there is no way of stating how much % of varies is explained by MDS axis

Appendix

knitr::opts_chunk$set(echo = FALSE)
library(ggplot2)
library(dplyr)
library(reshape2)
library(MASS)
library(plotly)
library(xlsx)

olive_data <- read.csv("olive.csv")
olive_data <- olive_data[,-1]

olive_data$Region <- factor(olive_data$Region, levels = c(1,2,3))

knitr::opts_chunk$set(echo = TRUE)
ggplot(data = olive_data, aes(x = oleic, y = palmitic), colour = linolenic) + geom_point(aes(colour = linoleic)) + ggtitle("Scatter plot of palmitic vs. oleic coloured by linolenic")
ggplot(data = olive_data, aes(x = oleic, y = palmitic)) + geom_point(aes(colour = cut_interval(linoleic, n = 4))) + ggtitle("Scatter plot of palmitic vs. oleic coloured by 4 intervals of linolenic")

ggplot(data = olive_data, aes(x = oleic, y = palmitic)) + geom_point(aes(colour = cut_interval(linolenic, n = 4))) + ggtitle("Scatter plot of palmitic vs. oleic coloured by 4 intervals of linolenic")


ggplot(data = olive_data, aes(x = oleic, y = palmitic)) + geom_point(aes(size = cut_interval(linolenic, n = 4))) + ggtitle("Scatter plot of palmitic vs. oleic sized by 4 intervals of linolenic")

ggplot(data = olive_data, aes(x = oleic, y = palmitic)) + geom_point() +  geom_spoke(aes(angle = as.numeric(cut_interval(linolenic, n = 4))*10), radius = 50) + ggtitle("Scatter plot of palmitic vs. oleic spoke angles by 4 intervals of linolenic")

ggplot(data = olive_data, aes(x = oleic, y = eicosenoic)) + geom_point(aes(colour = as.numeric(Region))) + ggtitle("Scatter plot of palmitic vs. oleic, coloured by region as number")

ggplot(data = olive_data, aes(x = oleic, y = eicosenoic)) + geom_point(aes(colour = Region)) + ggtitle("Scatter plot of palmitic vs. oleic, coloured by region as factors")                                                                       

ggplot(data = olive_data, aes(x = oleic, y = eicosenoic)) + geom_point(aes(colour = cut_interval(linoleic, n = 3), shape = cut_interval(palmitic, n = 3), size = cut_interval(palmitoleic, n = 3)))
ggplot(data = olive_data, aes(x = oleic, y = eicosenoic)) + geom_point(aes(colour = Region, shape = cut_interval(palmitic, n = 3), size = cut_interval(palmitoleic, n = 3)))

olive_data_sum <- olive_data %>% group_by(Region) %>% summarise(palmitic = sum(palmitic),
                                                     palmitoleic = sum(palmitoleic),
                                                     stearic = sum(stearic),
                                                     oleic = sum(oleic),
                                                     linoleic = sum(linoleic),
                                                     linolenic = sum(linolenic),
                                                     arachidic = sum(arachidic),
                                                     eicosenoic = sum(eicosenoic))


olive_data_sum_long <- melt(olive_data_sum, id.vars = c("Region"))

olive_data_sum_long %>% group_by(Region) %>% plot_ly(labels = ~variable, values = ~value, 
                                                     type = 'pie', showlegend = FALSE) %>% layout(title = 'Total oils by region', 
                                                                                                  xaxis = list(showgrid = FALSE, zeroline = FALSE, showticklabels = FALSE), yaxis = list(showgrid = FALSE, zeroline = FALSE, showticklabels = FALSE))
ggplot(olive_data, aes(x = linoleic, y = eicosenoic)) + geom_point(aes(colour = Region)) + geom_density_2d()

ggplot(olive_data, aes(x = linoleic, y = eicosenoic)) + geom_point(aes(colour = Region))
baseball <- read.xlsx("baseball-2016.xlsx", sheetName = "Sheet1")
distance <- dist(baseball[, !names(baseball) %in% c("Team", "League")] , method = "minkowski")
fit <- isoMDS(distance, k = 2, maxit = 100)

baseball$MDS1 <- fit$points[,1]
baseball$MDS2 <- fit$points[,2]

# plotly plot
baseball %>% plot_ly(type = "scatter", 
                     mode = "markers", 
                     colors = "Set1",
                     showlegend = T) %>% add_trace(x = ~MDS1, y = ~MDS2, color = ~League, text = ~Team) %>% layout(title = "Non Metric MDS plot")



sh <- Shepard(distance, fit$points)
Original_Dist <-as.numeric(distance)
MDS_Dist <- as.numeric(dist(fit$points))

rownames(baseball) <- baseball$Team

n=nrow(fit$points)
index=matrix(1:n, nrow=n, ncol=n)
index1=as.numeric(index[lower.tri(index)])

n=nrow(fit$points)
index=matrix(1:n, nrow=n, ncol=n, byrow = T)
index2=as.numeric(index[lower.tri(index)])

plot_ly()%>%
  add_markers(x=~Original_Dist, y=~MDS_Dist, hoverinfo = 'text', name = "Datapoints",
        text = ~paste('Obj1: ', rownames(baseball)[index1],
                      '<br> Obj 2: ', rownames(baseball)[index2]))%>%
  #if nonmetric MDS inolved
  add_lines(x=~sh$x, y=~sh$yf, name="Stress")

MDS_plotter <- function(MDS_axis, Col){
  df <- cbind(baseball[[MDS_axis]], baseball[[Col]], baseball$League, baseball$Team)
  df <- as.data.frame(df)
  names(df) <- c(eval(MDS_axis),eval(Col), "League", "Team")
  df$League <- as.character(df$League)
  
    # plotly plot
  y_title <- list(title = Col)
  x_title <- list(title = MDS_axis)
   
  plot_return <- df %>% plot_ly(type = "scatter", mode = "markers", colors = "Set1", showlegend = T) %>% 
    add_trace(x = df[,1], y = df[,2], color = ~League, text = ~Team) %>% 
    layout(title = "Plot of MDS axis vs. variable", yaxis =y_title, xaxis=x_title)
  return(plot_return)
}

# Plotting MDS on all numeric columns
# MDS axis 1
# MDS_plotter("MDS1", "Won")
# MDS_plotter("MDS1", "Lost")
# MDS_plotter("MDS1", "Runs.per.game")
# MDS_plotter("MDS1", "HR.per.game")
# MDS_plotter("MDS1", "AB")
# MDS_plotter("MDS1", "Runs")
# MDS_plotter("MDS1", "Hits")
# MDS_plotter("MDS1", "X2B")
# MDS_plotter("MDS1", "X3B")
# MDS_plotter("MDS1", "HR")
# MDS_plotter("MDS1", "RBI")
# MDS_plotter("MDS1", "StolenB")
# MDS_plotter("MDS1", "CaughtS")
# MDS_plotter("MDS1", "BB")
# MDS_plotter("MDS1", "SO")
# MDS_plotter("MDS1", "BAvg")
# MDS_plotter("MDS1", "OBP")
# MDS_plotter("MDS1", "SLG")
# MDS_plotter("MDS1", "OPS")
# MDS_plotter("MDS1", "TB")
# MDS_plotter("MDS1", "GDP")
# MDS_plotter("MDS1", "HBP")
# MDS_plotter("MDS1", "SH")
# MDS_plotter("MDS1", "SF")
# MDS_plotter("MDS1", "IBB")
# MDS_plotter("MDS1", "LOB")
# 
# # MDS axis 2
# MDS_plotter("MDS2", "Won")
# MDS_plotter("MDS2", "Lost")
# MDS_plotter("MDS2", "Runs.per.game")
# MDS_plotter("MDS2", "HR.per.game")
# MDS_plotter("MDS2", "AB")
# MDS_plotter("MDS2", "Runs")
# MDS_plotter("MDS2", "Hits")
# MDS_plotter("MDS2", "X2B")
# MDS_plotter("MDS2", "X3B")
# MDS_plotter("MDS2", "HR")
# MDS_plotter("MDS2", "RBI")
# MDS_plotter("MDS2", "StolenB")
# MDS_plotter("MDS2", "CaughtS")
# MDS_plotter("MDS2", "BB")
# MDS_plotter("MDS2", "SO")
# MDS_plotter("MDS2", "BAvg")
# MDS_plotter("MDS2", "OBP")
# MDS_plotter("MDS2", "SLG")
# MDS_plotter("MDS2", "OPS")
# MDS_plotter("MDS2", "TB")
# MDS_plotter("MDS2", "GDP")
# MDS_plotter("MDS2", "HBP")
# MDS_plotter("MDS2", "SH")
# MDS_plotter("MDS2", "SF")
# MDS_plotter("MDS2", "IBB")
# MDS_plotter("MDS2", "LOB")

# Best plots are with MDS-2 with variables HR.per.game and HR
MDS_plotter("MDS2", "HR.per.game")
MDS_plotter("MDS2", "HR")